GPEC: A Real-Time–Capable Tokamak Equilibrium Code

Abstract

A new parallel equilibrium reconstruction code for tokamak plasmas is presented. GPEC allows to compute equilibrium flux distributions sufficiently accurate to derive parameters for plasma control within 1 ms of runtime which enables real-time applications at the ASDEX Upgrade experiment (AUG) and other machines with a control cycle of at least this size. The underlying algorithms are based on the wellestablished offline-analysis code CLISTE, following the classical concept of iteratively solving the Grad-Shafranov equation and feeding in diagnostic signals from the experiment. The new code adopts a hybrid parallelization scheme for computing the equilibrium flux distribution and extends the fast, shared-memory-parallel Poisson solver which we have described previously by a distributed computation of the individual Poisson problems corresponding to different basis functions. The code is based entirely on open-source software components and runs on standard server hardware and software environments. The real-time capability of GPEC is demonstrated by performing an offline-computation of a sequence of 1000 flux distributions which are taken from one second of operation of a typical AUG discharge and deriving the relevant control parameters with a time resolution of a millisecond. On current server hardware the new code allows employing a grid size of 32 × 64 zones for the spatial discretization and up to 15 basis functions. It takes into account about 90 diagnostic signals while using up to 4 equilibrium iterations and computing more than 20 plasma-control parameters, including the computationally expensive safety-factor q on at least 4 different levels of the normalized flux.

Coupling of the Flux Diffusion Equation with the Equilibrium Reconstruction at ASDEX Upgrade

“…Another advantage of the present method compared to ASTRA and TRANSP is that it provides an interpretative free-boundary equilibrium where magnetic and other measured data (see below) are fitted. Additionally, the code is real-time capable in both parts, the GSE solver 11,12,13 and the current diffusion solver 5 , which is far beyond the scope of codes such as TRANSP and ASTRA. The primary goal is to provide equilibria with a temporal resolution of 1 ms for the full ASDEX Upgrade discharge of up to 10 s before the next discharge is launched typically after about 30 min.…”

“…Eq. ( 1) is solved with a parallel Grad-Shafranov solver capable for real-time control of tokamak plasmas 11,12,13 . The solver is embedded in the equilibrium package IDE (Integrated Data analysis Equilibrium) 8 .…”

An advanced plasma current tomography method based on Bayesian inference and neural networks for real-time application

“…received significant research attention. To date, several methods have been established for the reconstruction of plasma current distribution, which can be mainly divided into two types: physical models [1][2][3][4][5][6][7][8][9] that include solving the Grad-Shafranov equation with the least-squares method as the core; and computational models, mainly based on machine learning [10][11][12][13][14][15][16] and deep learning [17]. With the advancement of computational technologies, the computational power and performance are continuously increasing, and the latter models are becoming increasingly popular.…”

Nature of ideal MHD instabilities as described by multi-region relaxed MHD

“…This means an equilibrium code like the Variational Moments Equilibrium Code (VMEC) 14 based on the assumption of smooth pressure and current profiles can never strictly converge (though they can give a reasonable approximation quickly so VMEC has become the workhorse of stellarator design studies). A number of 3-D equilibrium codes which regularize, in various ways, such singular be-havior implied by IMHD have been written, such as IPEC 15 , PIES 16 , SIESTA 17 , HINT2 18 , and GPEC 19 .…”